What uniform annual payment for 30 years is equivalent to spending $10,000 immediately, $10,000 at the...

What uniform annual payment for 30 years is equivalent to spending $10,000 immediately, $10,000 at the end of 10 years, $10,000 at the end of 20 years, and $2,000 a year after 30 years? Assume an interest rate of 9%

*for 30 years

Expert Solution

Uniformal Annual Payment is $852.87

Working Note:

Step 1
We need to find out Annual payment for 30 years is equavalent to
1st	Spending 10,000 immediately	$ 10,000.00
2nd	10,000 at the end of 10 years = 10,000*(1+9%)^10	$ 23,673.64
3rd	10,000 at the end of 20 years = 10,000*(1+9%)^20	$ 56,044.11
4th	2,000 at the end of 30 years = 2,000*(1+9%)^30	$ 26,535.36
	Total Future Value		$ 116,253.10

Step 2	We need to find out FVA
		A = Annuity
		r = Interest rate
		n = Number of years
		Future Value of Annuity	$ 116,253.10
		Interest rate		9.00%
		No.of years		30

			FVA = A* (1+r)^n - 1 / r
			(1+r)^n-1 =	12.26767847
			r =	9.00%
			(1+r)^n - 1 / r	136.3075385
			116,253.10 = A * 136.3075385
			A = 116,253.10/136.3075385
			A=	$ 852.87

jeff jeffy answered 2 years ago

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